Question

Complete the steps to solve the inequality:

0.2(x + 20) – 3 > –7 – 6.2x

Use the distributive property:
Combine like terms:
Use the addition property of inequality:
Use the subtraction property of inequality:
Use the division property of inequality:




0.2x + 4 – 3 > –7 – 6.2x

0.2x + 1 > –7 – 6.2x

6.4x + 1 > –7

6.4x > –8

Answer 1

Let's go through the steps systematically to solve the inequality given:

Given inequality:
\[ 0.2(x + 20) - 3 > -7 - 6.2x \]

### Step 1: Use the distributive property

Distributing \(0.2\) in \(0.2(x + 20)\):
\[
0.2x + 4 - 3 > -7 - 6.2x
\]

This simplifies to:
\[
0.2x + 1 > -7 - 6.2x
\]

### Step 2: Combine like terms

Next, we'll continue the transformation:
\[
0.2x + 1 > -7 - 6.2x
\]
Now, we want to isolate the variable terms on one side. We'll move \(6.2x\) to the left side.

### Step 3: Use the addition property of inequality

Adding \(6.2x\) to both sides:
\[
0.2x + 6.2x + 1 > -7
\]
Combining like terms gives:
\[
6.4x + 1 > -7
\]

### Step 4: Use the subtraction property of inequality

Now, subtract \(1\) from both sides:
\[
6.4x > -8
\]

### Step 5: Use the division property of inequality

Finally, divide both sides by \(6.4\) (note that \(6.4 > 0\), so the direction of the inequality does not change):
\[
x > \frac{-8}{6.4}
\]

Simplifying \(\frac{-8}{6.4}\):
\[
x > -\frac{80}{64} = -\frac{5}{4} = -1.25
\]

### Final Answer
Thus, the solution to the inequality is:
\[
x > -1.25
\]